Question

if the speed of a particale is increase thrice , how will it's kinetic energy be affected​

Answer 1

We all know the formula for kinetic energy of a particle

KE = 1/2*m*v^2

So, this shows that Kinetic energy is directly proportional to the square of speed

Now, So, increasing the speed thrice the original means increasing the kinetic energy by 9 times.

However, this relation is obtained taking some approximations.

According to special Relativity, mass of any object increases with speed.

So, here increase in speed even three times has to be considered negligibly small so as to consider the mass remaining constant throughout the whole process.

Hope this helps you !

Answer 2

We know that Kinetic Energy (EK) = (1/2)*(Mass)(Velocity)² or,

EK = (mv²)/2 - eqn.1

Since, mass of an object will always remain constant, m = m in any case. NOw, if velocity is made thrice, New Velocity (v') = 3v

So, New kinetic energy (EK') = m*(3v)²/2 = 9mv²/2 - eqn.2

Dividing eqn.1. by eqn.2,

$\dfrac{EK}{EK'} = \dfrac{mv^2}{2} \div \dfrac{9mv^2}{2}\\\\\\= \dfrac{mv^2}{2} \times \dfrac{2}{9mv^2}\\\\\\= \dfrac{1}{9}\\\\\\\implies EK = \dfrac{EK'}{9}\\\\\\\implies EK' = 9 \times EK$

Thus, kinetic energy will become 9 times.